Answer
Displacement vectors must be perpendicular.
Work Step by Step
The general equation for the magnitude of resultant of two vectors is
$R=\sqrt {A^{2}+B^{2}+2AB\cos\theta}$
Consider the case in which vectors are perpendicular. $\theta=90^{\circ}$ and $\cos\theta=0$, therefore the term $2AB\cos\theta$ disappears and the equation reduces to the form
$R=\sqrt {A^{2}+B^{2}}$.
In our case, when displacements are perpendicular
$Resultant= \sqrt {(4\,m)^{2}+(3\,m)^{2}}=\sqrt {25\,m^{2}}=5\,m$
